The original title of this work translated as "Foundation of Algebraic Analysis." Kashiwara (Kyoto U., Japan) changed the title to more precisely reflect the nature of the text's contents and to signal his belief that "the microlocal point of view helps concrete calculations, as powerfully as the Cauchy integral formula provides the values of many definite integrals." Chapters cover basic properties of D -modules, characteristic varieties, construction of D -modules, their functorial properties, regular holonomic systems, b -functions, ring of formal microdifferential operators, microlocal analysis of holonomic systems, and microlocal calculus of b -functions. Translated from the Japanese work Daisu Kaiseki Gairon (2000). Annotation c. Book News, Inc., Portland, OR (booknews.com)